Alrighty. We know that segment IJ is a straight angle, meaning that it is 180 degrees. Angle KOJ is a right angle, which is 90 degrees. On the same segment, angle GOI is 31 degrees.
First, add GOI and KOJ together. 31+90=121 Then, subtract that from your straight angle. 180-121=59 degrees.
Measure of angle KOG is 59 degrees.
Now, take your straight angle again, and subtract JOH from it. 180-31=49 degrees.